A common practice in the exploration for oil, gas and other valuable minerals is to perform seismic exploration in which an acoustic wave is imparted to the earth (including the sea) at or near the surface. The wave travels into the earth and reflects at boundaries between layers of materials of differing acoustic impedance. The reflected waves travel upwardly and may be detected at or near the surface by pluralities of microphones. The signals output by the microphones can be analyzed to determine the time of travel of the acoustic wave from the source to the microphone, and used to generate a representation of the earth's subterranean structure. The recorded signal, referred to as a seismic "trace", can be interpreted by skilled persons to identify likely locations for deposits of oil, gas and other valuable minerals.
One problem which has plagued this seismic exploration art since its inception is the fact that the acoustic waves travel in all directions in the earth, resulting in numerous reflections being recorded. For example, in the ocean exploration case, the wave may travel first downwardly towards the ocean bottom, up again towards the surface, be reflected back down toward the bottom and reflected again before being received at a microphone or "hydrophone." Such a wave is called a "surface multiple" because it reaches the surface twice in its path from the source to the receiver. Surface multiples also occur when the wave travels first into the sea bed, reflects from an interface between rock layers of varying acoustic impedance, travels back upwardly to the surface, back downwardly to the sea bottom or again to an interface between rock layers of varying impedance, and only then up to the source. This too is referred to as a surface multiple. Multiples also occur where the wave is reflected within a given rock layer a plurality of times before being received at the surface. These multiples, however, are not considered surface multiples. It is found, however, that the surface multiples constitute most of the multiples which obscure true seismic events in the recorded hydrophone output signal, or "trace." Multiples can thus be considered as unwanted "noise" in the seismic record, since they obscure the seismic events of interest. Accordingly, it has for a long time been a well recognized need of the art to provide an effective method for removing surface multiples from the seismic record.
Various prior art methods have been tried for removal of surface multiples from recorded traces. It has been noted, for example, that the travel time for a surface multiple, the path of which is entirely in the water during an oceanographic expedition, is a function of the "offset", the distance between the source and receiver, and the number of times the multiple reflects from the surface. For example, if the multiple reflects from the surface once before being received by the microphone and the offset is zero, the multiple's travel time is exactly twice that of the principal waves. This fact has been used in various schemes to remove multiples.
Other methods involve complex ray tracing schemes which generate a synthetic multiple wave and subtract it. from the actual wave to obtain a supposedly multiple free record. However, these methods are very awkward in that they require significant knowledge of the subsea structure as well as the ocean bottom configuration before the synthetic wave can be generated. Similar synthetic multiples can be generated using more accurate methods not directly involving ray tracing, e.g., field propagation techniques, but again these require detailed knowledge of at least the ocean bottom, as well as the shape of the subsea interfaces, and so are not as practical as would be desired.